The origin of anomalous Hall effect in ferro(i)magnetic materials is explained by two possible mechanisms namely, extrinsic and intrinsic [1]}. The extrinsic mechanism further includes the contributions from skew scattering and side jump mechanism and is related to the scattering events. However, the intrinsic AHE is correlated to the electronic band structure of the material. Karplus and Luttinger [2]}, long ago in a classic work, have shown that the applied electric field combines with spin-orbit coupling to give an additional term (which is related to the Berry curvature) added to the usual electron velocity. This additional term is known to be anomalous velocity.
Though the intrinsic mechanism is purely of the band structure origin, due to certain scaling law, practically it is not possible to decouple the intrinsic and side jump mechanism and the latter has very small contribution to the AHC in comparison to the intrinsic part [3]}. The present work discusses the intrinsic anomalous Hall conductivity which has contributions only from Berry curvature which can be expressed (for the nth band) as follows [4]},
\(\Omega ^n_{xy}=\sum _{m\ne m}~\frac{Im[<\psi _{nk}|\hat{v}_x|\psi _{mk}><\psi _{mk}|\hat{v}_y|\psi _{nk}>]}{(\varepsilon _{nk}-\varepsilon _{mk})^2}\) 
